The present invention relates to computed tomography (CT) imaging apparatus; and more particularly, to techniques for reconstructing a image from X-ray attenuation data acquired by such apparatus.
In a computed tomography system, an X-ray source projects a fan-shaped pattern of beams, which is collimated to lie within an X-Y plane of a Cartesian coordinate system, termed the "imaging plane". The X-ray beams pass through the object being imaged, such as a medical patient, and impinge upon an array of radiation detectors. A beam of X-rays is defined as the radiation that strikes one of the detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the X-ray beam by the object and each detector produces a separate electrical signal that is a measurement of beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce an attenuation profile.
The source and detector array in a common type of CT system are rotated on a gantry within the imaging plane and around the object so that the angle at which the X-ray beam intersects the object constantly changes. A group of X-ray attenuation measurements from the detector array at a given angle form a "projection" and a "scan" of the object comprises a set of projections made at different angular orientations during approximately a half or a full revolution of the X-ray source and detector. The gantry may stop or continue to move as the measurements are being made.
The resultant projections from the scan are used to reconstruct an image which reveals the anatomical structures in a slice taken through the object. The prevailing method for reconstructing image is referred to in the art as the filtered backprojection technique. This process converts the attenuation measurements from a scan into integers called "CT numbers" or "Hounsfield units", which are used to control the brightness of a corresponding pixel on a cathode ray tube display or on photographic film.
It is desirable to produce an image having as high resolution as possible. Spatial resolution of the reconstructed image is dependent, in part, on the width of each X-ray beam at the center of the imaged object. This beam width, which varies with the distance from the source and the detector, is determined primarily by the source width, the size of the focal spot on an anode of the X-ray tube, the geometry of the scanner, and the aperture of each detector. The averaging affect of a generally rectangular beam of width a, bandlimits the received image to a spatial frequency of 1/a and less.
The beam spacing, defined near the center of the imaged object and determined by the detector pitch, controls the spatial sampling frequency of the CT system. Given the spatial bandlimit of 1/a, the sampling frequency must be approximately 2/a, per the Nyquist sampling theorem, to avoid aliasing effects in the reconstructed image. The elimination of aliasing requires that the beam be sampled or read at distances separated by one-half the beam width. Ordinarily, the beam width is optimized to be substantially equal to the beam spacing and therefore sampling is ideally performed no less than twice per beam spacing. Henceforth referred to as "double sampling."
A conceptually simple way to accomplish double sampling is to shift the detectors one-half of their pitch after a first sample and then take a second sample. In this way each beam is sampled twice in its width (and spacing). Nevertheless, mechanical problems incident to rapidly and precisely moving the detectors by one-half their pitch (typically on the order of 1 mm) make this approach impractical.
Another method has been proposed as described in U.S. Pat. No. 5,173,852 entitled "Computed Tomography System with Translatable Focal Spot." This double sampling process is to wobble the X-ray source by an amount that will shift each beam by one-half its spacing. The wobbling is generally within the plane of rotation of the gantry and along the tangent to the gantry rotation. Wobbling of the X-ray source is easily accomplished electrostatically or electromagnetically without mechanical motion of the X-ray source. The source typically is an X-ray tube, in which an electron beam is accelerated against an anode at a focal spot to produce X radiation emanating from the focal spot. The focal spot may be moved on the surface of the anode by the use of deflection coils or electrodes within the X-ray tube which deflect the electron beam by the creation of a local magnetic or electrostatic field, as is well understood in the art.
Double sampling is performed by acquiring a second set of projections offset from the first set by one-half the pitch of the detectors. After acquiring a projection in the first set, a projection for the second set is acquired after the gantry moves an odd multiple of one-half the width of a detector (e.g. one half the width) and the focal spot is wobbled. The another projection is acquired for the first set after the gantry moves another amount equal to an odd multiple of one-half the width of a detector, or the full width of a detector from the location at which the previous projection for the first set was acquired. At this time the focal spot is wobbled back to its previous position on the anode surface. This alternating acquisition continues throughout the scan finally resulting in two interleaved sets of projections.
The two sets of projections were processed individually to reconstruct a pair of separate images. For example, conventional backprojection image reconstruction was performed on each set. The two reconstructed images then were added together to form a single image that is freer of aliasing artifacts than either image alone.
During the backprojection image reconstruction if a given picture element in the image lies directly on an X-ray beam extending between the focal spot and a detector in a given projection, then the projection data sample from the detector is used to form that picture element. However, if the picture element lies between two beams, then the samples from the detectors associated with those beams are used to form that picture element. For example, bi-linear interpolation is applied to the two detector samples to calculate a pseudo output that would have been produced by an imaginary detector if the pixel did lie directly on a beam of the X-ray beam. The two samples from the real detectors are weighted based on the relative position of the imaginary detector with respect to each real one.
This reconstruction technique introduces resolution degradation and a Moire pattern into the image. The image degradation is apparent from a point spread function of the bi-linear interpolation process as graphically depicted in FIGS. 1A-1C. FIGS. 1A and 1B represent the point spread function for each set of projections with each vertical mark on the horizontal axes representing the center of a detector. Note that if the picture element is aligned with detector X or Y, the weighting factor is one for that detector and zero for the adjacent detectors. Likewise, if the picture element is aligned midway between two detectors, the outputs from each detector are weighted by one-half when forming the picture element. The resulting point spread function in FIG. 1C is produced by averaging the individual the point spread functions in FIGS. 1A and 1B, since the final step of the image reconstruction process averages the two reconstructed images. It is apparent from this graph that the point spread function behaves quite well at the center, but performs poorly at the boundaries. The long tails exhibited at the edges of the function contribute to the degradation of image resolution.